The regularized long wave equation (RLW) is solved numerically by using the quintic B-spline Galerkin finite element method. The same method is applied to the time-split RLW equation. Comparison is made with both analytical solutions and some previous results. Propagation of solitary waves, interaction of two solitons are studied. © 2005 Elsevier B.V. All rights reserved. MSC: 65N30; 65D07; 76B25

The aim of this paper is to test different types of spatial interpolation for the materialpoint method. The interpolations include quadratic elements and cubic splines. A brief introduction to the material-point method is given. Simple liner-elastic problems are tested, including the classical cantilevered beam problem. As shown in the paper, the use of negative shape functions is not consisten...

A dyadic algorithm for diagonalizing an arbitrary positive definite band matrix, referred to as a Gramian, is obtained efficiently orthogonalize the B-splines. The can be also used fast inversion method Gramian characterized by remarkable sparsity of matrix. There are two versions algorithm: first one more efficient and applicable Toeplitz while second general, works with any but computationall...

In this paper we consider spaces of bivariate splines of bi–degree (m,n) with maximal order of smoothness over domains associated to a two–dimensional grid. We define admissible classes of domains for which suitable combinatorial technique allows us to obtain the dimension of such spline spaces and the number of tensor–product B–splines acting effectively on these domains. Following the strateg...